Finite Group Databasebeta

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C₂×#72240977 #72344168

order	6144
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×#72240977

Splittings

C₂×#72236873 ⋊ C₃

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂×D₄×#120⋊C₃
commutator, cosocle	#585	C₂⁵×C₃
Frattini	C₂²×C₄	C₂⁵×A₄
Fitting	C₂×#72236873	C₃
hypercenter	C₂×AGL(1,ℤ/8)	#120⋊C₃
hypocenter	H(5,𝔽₂)	C₂³×C₃×D₄
LCS	G ▷ #585 ▷ H(5,𝔽₂)
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Only the 1356 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.